On the choice of a truncation point in fourier series density estimation

Abstract

A new method of estimating the truncation point which minimizes the mean integrated squared error (MISF) of a Fourier series density estimator is proposed The similarity of the new method to Akaike’s (1974) AIC procedure for estimating the dimension of a statistical model suggests a second method of choosing a truncation point.It is shown that both of the new methods lead to consistent estimation of the underlying density.A simulation study indicates that for certain density functions the new methods are an improvement over the original method of Kronmal and Tarter (1968).

Keywords:

• Probability density estimation
• Fourier series methods
• optimal truncation point